Static and dynamic axial crushing of prismatic thin-walled metal columns

Document Type : Research Paper


Department of Mechanical Engineering, Shahid Chamran University of ahvaz, Ahvaz, Iran


In this paper, a novel approach is proposed to investigate the progressive collapse damage of prismatic thin walled metal columns with different regular cross sections, under the action of axial quasi-static and impact loads. The present work mainly focuses on implementation of some important factors which have been neglected in other studies. These factors include the effect of reducing impactor velocity and inertia effect during collapse, a mixed collapse mode for crushing mechanism, and consideration of a realistic elasto-plastic model for material. Taking all these factors into account, the analysis led to some parametric algebraic equations without a possible general solution in terms of collapse variables. Consequently, a new theoretical approach was proposed based on previously offered Super Folding Element (SFE) theory, to obtain the closed form explicit relations for the static and dynamic mean crushing forces and collapse variables. The proposed approach considers an analytic-numeric discretization procedure to solve these equations. To evaluate the results, a detailed finite element analysis on square mild steel models was conducted under an axial impact load, using LS-DYNA and ANSYS software programs. Comparison of the experimental results that are available in the literature with those of finite element analysis, shows the applicability of this approach in predicting the collapse behavior in such structures.


Main Subjects

[1]           J. Alexander, An approximate analysis of the collapse of thin cylindrical shells under axial loading, The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 13, No. 1, pp. 10-15, 1960.
[2]           T. Wierzbicki, W. Abramowicz, On the crushing mechanics of thin-walled structures, Journal of Applied mechanics, Vol. 50, No. 4a, pp. 727-734, 1983.
[3]           W. A. N. Jones, W. Abramowicz, Dynamic axial crushing of square tubes, International Journal of Impact Engineering, Vol. 2, pp. 179-208, 1984.
[4]           W. Abramowicz, T. Wierzbicki, Axial crushing of multicorner sheet metal columns, Journal of Applied Mechanics, Vol. 56, No. 1, pp. 113-120, 1989.
[5]           M. White, N. Jones, W. Abramowicz, A theoretical analysis for the quasi-static axial crushing of top-hat and double-hat thin-walled sections, International Journal of Mechanical Sciences, Vol. 41, No. 2, pp. 209-233, 1999.
[6]           A. Najafi, M. Rais-Rohani, Mechanics of axial plastic collapse in multi-cell, multi-corner crush tubes, Thin-Walled Structures, Vol. 49, No. 1, pp. 1-12, 2011.
[7]           W. Hao, J. Xie, F. Wang, Theoretical prediction of the progressive buckling and energy absorption of the sinusoidal corrugated tube subjected to axial crushing, Computers & Structures, Vol. 191, pp. 12-21, 2017.
[8]           W. Hong, F. Jin, J. Zhou, Z. Xia, Y. Xu, L. Yang, Q. Zheng, H. Fan, Quasi-static axial compression of triangular steel tubes, Thin-Walled Structures, Vol. 62, pp. 10-17, 2013.
[9]           G. Martínez, C. Graciano, P. Teixeira, Energy absorption of axially crushed expanded metal tubes, Thin-Walled Structures, Vol. 71, pp. 134-146, 2013.
[10]         T. Wierzbicki, W. Abramowicz, The mechanics of deep plastic collapse of thin walled structures, Jones N, Wierzbicki T, editors. Structural failure, pp. 281–329, 1989.
[11]         X. Zhang, H. Huh, Crushing analysis of polygonal columns and angle elements, International Journal of Impact Engineering, Vol. 37, No. 4, pp. 441-451, 2010.
[12]         X. Zhang, H. Zhang, Crush resistance of square tubes with various thickness configurations, International Journal of Mechanical Sciences, Vol. 107, pp. 58-68, 2016.
[13]         J. Song, Y. Zhou, F. Guo, A relationship between progressive collapse and initial buckling for tubular structures under axial loading, International Journal of Mechanical Sciences, Vol. 75, pp. 200-211, 2013.
[14]         S. Liu, Z. Tong, Z. Tang, Y. Liu, Z. Zhang, Bionic design modification of non-convex multi-corner thin-walled columns for improving energy absorption through adding bulkheads, Thin-Walled Structures, Vol. 88, pp. 70-81, 2015.
[15]         Y. Tao, S. Duan, W. Wen, Y. Pei, D. Fang, Enhanced out-of-plane crushing strength and energy absorption of in-plane graded honeycombs, Composites Part B: Engineering, Vol. 118, pp. 33-40, 2017.
[16]         M. Macaulay, R. Redwood, Small scale model railway coaches under impact, The Engineer, Vol. 218, pp. 1041-1046, 1964.
[17]         A. Pugsley, The crumpling of tubular structures under impact conditions, in Proceeding of, 33-41.
[18]         A. Coppa, New ways to soften shock, Machine Design, Vol. 28, pp. 130-140, 1968.
[19]         A. A. Ezra, An assessment of energy absorbing devices for prospective use in aircraft impact situations, in Proceeding of, Pergamon Press, pp.
[20]         S. Reid, T. Reddy, Axially loaded metal tubes as impact energy absorbers,  in: Inelastic behaviour of plates and shells, Eds., pp. 569-595: Springer, 1986.
[21]         W. Abramowicz, N. Jones, Dynamic progressive buckling of circular and square tubes, International Journal of Impact Engineering, Vol. 4, No. 4, pp. 243-270, 1986.
[22]         W. Abramowicz, Thin-walled structures as impact energy absorbers, Thin-Walled Structures, Vol. 41, No. 2, pp. 91-107, 2003.
[23]         J. Fang, Y. Gao, G. Sun, N. Qiu, Q. Li, On design of multi-cell tubes under axial and oblique impact loads, Thin-Walled Structures, Vol. 95, pp. 115-126, 2015.
[24]         H. Sun, J. Wang, G. Shen, P. Hu, Energy absorption of aluminum alloy thin-walled tubes under axial impact, Journal of Mechanical Science and Technology, Vol. 30, No. 7, pp. 3105-3111, 2016.
[25]         D. Karagiozova, M. Alves, Dynamic elastic-plastic buckling of structural elements: a review, Applied Mechanics Reviews, Vol. 61, No. 4, pp. 040803, 2008.
[26]         T. Tran, S. Hou, X. Han, M. Chau, Crushing analysis and numerical optimization of angle element structures under axial impact loading, Composite Structures, Vol. 119, pp. 422-435, 2015.
[27]         C. Zhou, B. Wang, J. Ma, Z. You, Dynamic axial crushing of origami crash boxes, International journal of mechanical sciences, Vol. 118, pp. 1-12, 2016.
[28]         M. Costas, J. Díaz, L. Romera, S. Hernández, A multi-objective surrogate-based optimization of the crashworthiness of a hybrid impact absorber, International Journal of Mechanical Sciences, Vol. 88, pp. 46-54, 2014.
[29]         S. Ebrahimi, N. Vahdatazad, Multiobjective optimization and sensitivity analysis of honeycomb sandwich cylindrical columns under axial crushing loads, Thin-Walled Structures, Vol. 88, pp. 90-104, 2015.
[30]         A. Jusuf, T. Dirgantara, L. Gunawan, I. S. Putra, Crashworthiness analysis of multi-cell prismatic structures, International Journal of Impact Engineering, Vol. 78, pp. 34-50, 2015.
[31]         A. P. Meran, T. Toprak, A. Mu─čan, Numerical and experimental study of crashworthiness parameters of honeycomb structures, Thin-Walled Structures, Vol. 78, pp. 87-94, 2014.
[32]         M. Bambach, M. Elchalakani, Plastic mechanism analysis of steel SHS strengthened with CFRP under large axial deformation, Thin-walled structures, Vol. 45, No. 2, pp. 159-170, 2007.
[33]         A. Farajpour, A. Rastgoo, M. Farajpour, Nonlinear buckling analysis of magneto-electro-elastic CNT-MT hybrid nanoshells based on the nonlocal continuum mechanics, Composite Structures, Vol. 180, pp. 179-191, 2017.
[34]         A. Rajaneesh, I. Sridhar, S. Rajendran, Relative performance of metal and polymeric foam sandwich plates under low velocity impact, International Journal of Impact Engineering, Vol. 65, pp. 126-136, 2014.
[35]         L. Aktay, A. K. Toksoy, M. Güden, Quasi-static axial crushing of extruded polystyrene foam-filled thin-walled aluminum tubes: experimental and numerical analysis, Materials & design, Vol. 27, No. 7, pp. 556-565, 2006.
[36]         M. Shishesaz, M. Kharazi, P. Hosseini, M. Hosseini, Buckling Behavior of Composite Plates with a Pre-central Circular Delamination Defect under in-Plane Uniaxial Compression, Journal of Computational Applied Mechanics, Vol. 48, No. 1, pp. 12, 2017.
[37]         B. W. Schafer, The direct strength method of cold-formed steel member design, Journal of constructional steel research, Vol. 64, No. 7-8, pp. 766-778, 2008.
[38]         B. Schafer, Local, distortional, and Euler buckling of thin-walled columns, Journal of structural engineering, Vol. 128, No. 3, pp. 289-299, 2002.
[39]         S. P. Timoshenko, Stability of bars, plates, and shells, International Applied Mechanics, Vol. 7, No. 10, pp. 1175-1176, 1971.
Volume 50, Issue 1
June 2019
Pages 27-40
  • Receive Date: 30 January 2018
  • Revise Date: 20 May 2018
  • Accept Date: 11 June 2018